Least Common Multiple (LCM) of 24 and 178
The least common multiple (LCM) of 24 and 178 is 2136.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 24 and 178?
First, calculate the GCD of 24 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 178 = 0 remainder 24 |
| 2 | 178 ÷ 24 = 7 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 37 | 6771 |
| 22 and 21 | 462 |
| 158 and 169 | 26702 |
| 109 and 144 | 15696 |
| 38 and 167 | 6346 |